Public Finance, 2nd Edition

other), and pareto optimality would still be described by this rule. Further-

more, the subset of people whose consumption generates consumer external-

ities could number far fewer than H people. There may only be one such

person. As a practical matter, the government would only intervene if the

number of people aVected by a particular externality was fairly large and/or

the externalities generated in any one instance were deemed to be ``substan-

tial'' in some sense. Very few goods (factors) are likely to meet this practical

criterion. That is, most goods are certainly well toward the pole of pure

privateness. Private bargaining may be the preferred solution when the

numbers aVected are small if, indeed, any action can hope to improve the

private market outcomes given the transactions costs of bargaining or gov-

ernment intervention.

All these considerations serve to mitigate the actual policy problems

caused by consumption externalities. Nonetheless, if, for example, J people

were aVected by each of L goods as described by the model, then J  L taxes

(subsidies) are required for allocative eYciency, a formidable task even if

both J and L are ``fairly small'' relative to all the people and all the goods and

factors in the economy.

We have been analyzing the case of individualized externalities, in which

the external eVects associated with private sector activity depend not only on

what the activity is but who is doing it: It matters who builds a fence. The

inescapable conclusion is that neither government taxes and subsidies nor

private bargaining can be expected to achieve the pareto-optimal conditions

for any individualized externality in which the external eVects are widespread.

Not all externalities are individualized, however. The Wnal two sections

of the chapter consider two common types of externalities that are not

individualized: the nonexclusive good and the aggregate externality. The

aggregate externality is the more hopeful of the two from a policy perspective.

NONEXCLUSIVE GOODSÐTHE SAMUELSON MODEL

Paul Samuelson was the Wrst economist to analyze the problem of external-

ities using a formal general equilibrium model of social welfare maximization

for his analytical framework. He developed his model in the two articles

mentioned in Chapter 2,

8

and it is safe to say that no other single work has

been more inXuential to the development of public expenditure theory. For

this reason alone, his model deserves special attention in any treatise on

public sector economics. It also happens to be a useful vehicle for exploring

a number of important issues, including:

8

P. A. Samuelson, ``The Pure Theory of Public Expenditure,'' Review of Economics and

Statistics, November 1954; P. A. Samuelson, ``Diagrammatic Exposition of a Theory of Public

Expenditure,'' Review of Economics and Statistics, November 1955. See also P. A. Samuelson,

``Aspects of Public Expenditure Theories,'' Review of Economics and Statistics, November 1958.

170 NONEXCLUSIVE GOODSÐTHE SAMUELSON MODEL